This is a different algorithm with the above SGDA, and it is originally proposed for solving the convex-concave setting of min-max optimization problems by [1]}. Given \(z_t\)  as a base, we take a virtual gradient descent ascent step and obtain a \(\tilde{z}_t\) , which can be treated as the shadow of \(z_t\) . Then we use the gradient at \(z_t^{\prime }\)  as the update direction of \(z_t\) . This process can be described as:
\(\begin{aligned}z_t^{\prime }&=z_t+\gamma _t\cdot V(z_t;\omega _t^{(1)})\\z_{t+1}&=z_t+\gamma _t\cdot V(z_t^{\prime }; \omega _t^{(2)}).\end{aligned}[\mathrm {SEG}]\) 
